# Now on to quantum numbers…

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Now on to quantum numbers…

Quantum Numbers PRINCIPAL: n energy level,
the distance the orbital is from the nucleus (1, 2, 3, 4…) ANGULAR MOMENTUM: l shape (s = 0, p = 1, d = 2, f = 3) MAGNETIC: ml spatial orientation (0 for s; -1, 0, +1 for p; -2, -1, 0, +1, +2 for d, etc.) SPIN: ms spin (+1/2 or -1/2)

Review Atomic number = # electrons
Electrons occupy orbitals defined by n, l, m Each orbital can hold two electrons Orbitals  diffuse electron cloud “lower energy electron”  closer to nucleus Outer electrons: “valence” most reactive

Quantum Numbers The principal quantum number has the symbol n.
n = 1, 2, 3, 4, “shells” (n = K, L, M, N, ) The electron’s energy depends principally on n .

Quantum Numbers The angular momentum quantum number has the symbol .
 = s, p, d, f, g, h, (n-1)  tells us the shape of the orbitals. These orbitals are the volume around the atom that the electrons occupy 90-95% of the time.

Quantum Numbers The symbol for the magnetic quantum number is m, representing the spatial orientation. m = -  , (-  + 1), (-  +2), , , ( -2), ( -1),  If  = 0 (or an s orbital), then m = 0. If  = 1 (or a p orbital), then m = -1,0,+1. y z x

If  = 2 (or a d orbital), then m = -2,-1,0,+1,+2.
If  = 3 (or an f orbital), then m = -3,-2,-1,0,+1,+2, +3. Theoretically, this series continues on to g,h,i, etc

Spin quantum number The last quantum number is the spin quantum number which has the symbol ms. The spin quantum number only has two possible values. ms = +1/2 or -1/2

Spin of electron

Spin quantum number effects:
Every orbital can hold up to two electrons. Consequence of the Pauli Exclusion Principle. The two electrons are designated as having one spin up  and one spin down Spin describes the direction of the electron’s magnetic fields.

Re-Cap: Quantum Numbers
PRINCIPAL: n energy level, distance from nucleus (1, 2, 3, 4…) ANGULAR MOMENTUM: l shape (s = 0, p = 1, d = 2, f = 3) MAGNETIC: ml spatial orientation (0 for s; -1, 0, +1 for p; -2, -1, 0, +1, +2 for d, etc.) SPIN: ms spin (+1/2 or -1/2)

Atomic Orbitals: s, p, d, f Atomic orbitals are regions of space where the probability of finding an electron about an atom is highest. s orbital properties: There is one s orbital per n level.  = 0 and only one value of m = 0

s orbitals are spherically symmetric
For every s orbital: = 0 and ml = 0 The only thing that changes for s orbitals is n.

1s orbital of hydrogen Distance from nucleus

Probability densities for finding an electron at a given radius 1s, 2s, and 3s orbitals for hydrogen

Three dimensional depictions of electron distribution

p orbitals p orbital properties:
The first p orbitals appear in the n = 2 shell. p orbitals are peanut or dumbbell shaped volumes. There are 3 p orbitals per n level. The three orbitals are named px, py, pz.  = 1 for all p orbitals. m = -1,0,+1 (designate the three orientations)

p orbitals are peanut or dumbbell shaped.

p orbitals are peanut or dumbbell shaped.

2p orbital

d orbital properties: The five d orbitals have two different shapes:
The first d orbitals appear in the n = 3 shell. The five d orbitals have two different shapes: 4 are clover leaf shaped. 1 is peanut shaped with a doughnut around it. The orbitals lie directly on the Cartesian axes or are rotated 45o from the axes. There are 5 d orbitals per n level. The five orbitals are named: They have an  = 2. m = -2,-1,0,+1,+2 (5 values of m )

 = 2 m = -2,-1,0,+1,+2

 = 2 m = -2,-1,0,+1,+2 d orbital shapes

f orbital properties: The f orbitals have the most complex shapes.
The first f orbitals appear in the n = 4 shell. The f orbitals have the most complex shapes. There are seven f orbitals per n level. The f orbitals have complicated names. They have an  = 3 m = -3,-2,-1,0,+1,+2, values

 = 3 m = -3,-2,-1,0,+1,+2, values

f orbital shapes

Quantum Numbers PRINCIPAL: n energy level, distance from orbital (1, 2, 3, 4…) ANGULAR MOMENTUM: l shape (s = 0, p = 1, d = 2, f = 3) MAGNETIC: ml spatial orientation (0 for s; -1, 0, +1 for p; -2, -1, 0, +1, +2 for d, etc.) SPIN: ms spin (+1/2 or -1/2)

only s s and p s, p and d

Recall that Shrodinger’s equations derives the orbitals!

s, p, and d shells of a hydrogen atom

Pauli Exclusion Principle
No two electrons in an atom can have the same set of 4 quantum numbers.

The Aufbau Principle describes the electron filling order in atoms.

paired parallel spins

Electron Configurations

The order of orbital levels is:
1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s ….. Know configurations up to Ba!

Electron Configurations

Or you can use the periodic chart .
1 2 3 4 5 6

Or you can use the periodic chart .
1 2 3 4 5 6 Ge Ge = 1s22s22p63s23p64s23d104p2 or [Ar] 4s23d104p2 or [Ar]3d10 4s24p2

Hund’s rule tells us that the electrons will fill the
p orbitals by placing electrons in each orbital singly and with same spin until half-filled. Then the electrons will pair to finish the p orbitals.

3rd row elements

Fourth row

Fourth row

Fourth row

Fourth row

Specific quantum numbers for each electron

Specific quantum numbers for each electron

How to deal with ions? S vs S Cl vs Cl+

What type of ion would be expected to be favored for each element?
Na Na+ or Na- F F+ or F- What are the electron configurations of the two C isotopes? 12C 13C

Chemical properties  Valence electrons